1. Field of the Invention
This invention relates to an aid for teaching mathematics and more particularly multiplication, division and fractions.
2. Prior Art Statement
Currently, the most widely used approach to teaching mathematics involves having students watch a teacher explain concepts and solve sample problems on a chalkboard, a whiteboard, or via a TV screen (through videos or some kind of a PowerPoint presentation); and then the students are expected to be able to remember, reproduce, and generalize what they have seen. This highly visual method does not succeed with every student. According to recently published results in National Center for Education Statistics, National Report Card, Mathematics 2011, NATIONAL ASSESSMENT OF EDUCATIONAL PROGRESS AT GRADES 4 AND 8, NCES 2012-458, 2011, Figure C, page 2, only about thirty percent of eighth grade students (in the United States) score at a proficient level (or higher) on mathematics standardized tests. Therefore, some seventy percent of U.S. students could use a new approach, or many new approaches, to help them attain proficiency. Additionally, simple research conducted by Gordon Dryden and Jeannette Vos as detailed in chapter 3 and more particularly on page 130 in their book “UNLIMITED, The New Learning Revolution and the Seven Keys to Unlock It,” November 2008 available from International Sales Office, The Learning Web Limited, P.O. Box 87209, Meadowbank, Auckland, New Zealand, finds that some twenty-five percent to forty percent of students are kinesthetic learners (as opposed to visual learners or auditory learners). Kinesthetic learners do not learn as well from straight visual methods, such as a PowerPoint presentation or the lectures mentioned above, but instead learn better by using something they can touch, feel, move with their hands, or get physically involved with. Critical to STEM (Science, Technology, Engineering and Mathematics) is a thorough understanding of the basics of mathematics. Therefore, there is an unfulfilled need for a simple mathematics teaching aid to advance STEM wherein a student may easily learn fractions, fractional equivalents and multiplication products.
It is known to provide a pair of concentric cylinders disposed over a pencil. The outer cylinder has a longitudinal slot with the series of numbers 1-9 immediately above the slot and has an aperture to the left of the series of numbers. The inner cylinder has a plurality of lines of numbers disposed longitudinally along the exterior surface that are products of multiplication, these lines aligned for display through the slot of the outer cylinder. Aligned in circumferential arrangement with the lines of numbers is an annular row of numbers 1-9. By rotating the inner cylinder with respect to the outer cylinder, the number appearing in the aperture will display all the products of that number multiplied by the series of numbers above the slot. For instance, see the U.S. Pat. No. 1,720,499 issued on Jul. 1, 1926 to William Walker. Though the device of Walker shows a multiplier and a series of multiplicands, a complete multiplication table is not present nor can a plurality of fractional equivalents of various sets be instantly displayed. Furthermore, the cylinders of the pencil of Walker can easily be lost rendering the device unusable. Thus, there is a need for an aid for teaching mathematical concepts comprising a plurality of elongated elements provided with numbers on at least one face thereof, the plurality of elements adapted to be arranged in a multiplicity of sets wherein the sets present ordered pairs of fractions, multiplication products and division products.
It is known to provide a rod that has a plurality of identical shapes slidable but non rotatable upon the rod. Every facet of each shape has the same number but may have a different color. For instance, see the U.S. Pat. No. 7,828,553 issued on Nov. 9, 2010 to Carla Berg. The device is said to teach students counting by sets however, there is no means of placing pairs of rods together to teach fractions or to present a complete multiplication table. Additionally, the separate rods do not lend themselves to be instantly configured into varied sets and may also be misplaced. Accordingly, there is a need for an aid for teaching mathematical concepts comprising a plurality of elongated elements provided with numbers on at least one face thereof wherein the plurality of elements are joined together and adapted to be arranged in a multiplicity of sets to readily present ordered pairs of fractions, multiplication products and division products.
It is also known to provide a plurality of equal sized weights used on a balance beam to teach math concepts. By using fractional sized weights, fractional math may be taught. For instance, see the U.S. Pat. No. 3,949,491 issued on Apr. 13, 1976 to James Richard Harte. It is readily apparent that the plurality of parts may easily be lost and thus render the device unfit for continued use. Furthermore, no complete fractional table or plurality of fractional equivalents may be shown nor can the balance beam be utilized to display varied sets of fractions. Therefore, the need for a mathematics teaching aid that comprises a plurality of elongated elements flexibly joined together wherein each element is placeable adjacent any other element thus presenting a plurality of fractional units to a learner manipulating said plurality of elongated elements.
It is further known to provide an abacus frame carrying polygonal blocks having letters and numerals rotatably disposed upon the wires of the frame. Math principles may be taught by properly rotating the blocks to present sums, remainders, products and quotients. For instance, see the U.S. Pat. No. 422,612 issued on Mar. 4, 1890 to Christiana Neuhaus. Though fractions are shown on some blocks, showing fractions comprised of whole numbers is difficult and beyond the scope of the invention. Furthermore, a complete multiplication table is not available nor can the device be instantly reconfigured into fractional sets. Therefore, there has long been a need for a tool for teaching multiplication, division and fractions comprised of a plurality of elongated bars of specific cross sectional shape, at least one longitudinal face of each elongated bar provided with a first number adjacent one end and multiples of the first number disposed at spaced intervals along the longitudinal face where the elongated bars may be joined together in any sequence.
Likewise, it is known to provide a flat case with a multiplication table printed on one half of a base wherein the multiplication table may be observed through slots in a cover plate. Numbers from 1-10 are printed along the left side and across the top of the one half of the cover plate. Opaque slides are provided to slide within the slots of the cover plate. For instance, see the U.S. Pat. No. 6,769,914 B2 issued on Aug. 3, 2004 to Kalyani Sundararajan. Though equivalent fractions of adjacent sets of numbers may be displayed, there is no means to display equivalent fractions of non-adjacent sets as the device may not be reconfigured to place any number row adjacent any other number row. Obviously, there is still a great need for an aid for teaching mathematical concepts comprising a plurality of elongated elements provided with numbers on at least one face thereof with the plurality of elements adapted to be arranged in a multiplicity of sets thus presenting ordered pairs of fractions, multiplication products and division products to a student manipulating the elements into the different sets.
Yet another known teaching device is a flat case with a plurality of square channels disposed through one edge. The opposed edge is blocked. Numbers 1-9 are printed on the face of the case aligned with each channel. Adjacent each number are two apertures through the face of the case. Next to the second aperture is the equality sign. In the first channel, a third aperture is disposed through the case and diagonally from the third aperture in the first channel are third apertures in each of the remaining channels. Each bar is provided with one of the four math symbols that appears in the first aperture and adjacent the math symbol is a number. Each bar has a different number in the second position such that any bar may be inserted into any channel For instance, see the U.S. Pat. No. 3,743,750 issued on Jul. 3, 1973 to Motoi Hurue. As the blocks need to inserted into and removed from the channels, the likelihood of loss is great. Additionally, fractions and fractional equivalents may not be taught using this device. Apparently, the need for a flexible tool table that may be readily manipulated into multiple configurations showing various fractions and fractional equivalents is still great.
Fractional strips have long been used, and are still being used to show how many fractional units of a given size make up a whole. For instance, see the U.S. Pat. No. 1,174,689 issued on Mar. 7, 1916 to Frank J. Coleman. Equivalent fractions cannot be taught with this device. Additionally, the multiple parts may easily be misplaced. Furthermore, there is no multiplication table so the need for an integrated teaching aid showing a complete multiplication table with equivalent fractions on adjacent pairs of elements which can also be reconfigured to show equivalent fractions ofnon adjacent pairs of elements.